Find the m < t rounded to the nearest degree
1 answer:
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We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ =
π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.
R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14
a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = <span>π r² h
</span><span>V₁ = </span>3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³
b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × <span>V₂
</span>Vₐ = 3 × <span> π r³
</span>Vₐ = 3 × 3.14<span> (6.5 cm)³</span>
Vₐ = 3,449.3 cm³
c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V =
×100
V =
×100
V = 0.6666 ×100
V = 66.66%
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ =
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.
R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14
a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = <span>π r² h
</span><span>V₁ = </span>3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³
b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × <span>V₂
</span>Vₐ = 3 × <span>
</span>Vₐ = 3 ×
Vₐ = 3,449.3 cm³
c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V =
V =
V = 0.6666 ×100
V = 66.66%
Answer:
none of the above
Step-by-step explanation:
The grocer's revenue will be the product of the number of loaves sold (30-2x) and their price (2.50+0.50x).
Revenue will be positive for values of x between those that make these factors be zero. The number of loaves sold will be zero when ...
... 30 -2x = 0
... 15 -x = 0 . . . . . divide by 2
... x = 15 . . . . . . . add x
The price of each loaf will be zero when ...
... 2.50 +0.50x = 0
... 5 + x = 0 . . . . . . . multiply by 2
... x = -5 . . . . . . . . . . subtract 5
Revenue will be positive for any number of increases greater than -5 and less than 15.
_____
D is the best of the offered choices, but it is incorrect in detail. -5 is a number less than 15, but will give zero revenue.
